Conan would get drunk and bed women after long quests and adventures.
Meaning death by assassination by such means would only be in effect 1/100 in his everyday life.
In between he is on horseback traveling the land entering cities and coming under contact of many varied people.
The OP states that Conan is simply unaware of an attack. And without a scenario or setting for such a battle we must assume that Conan is at least awake and at least in a situation where he could be ready for battle.
To assume this fight takes place under a worse case scenario where Conan is drunk and carrying two women on each shoulder in a random alleyway makes this fight odd. And even if he is in this situation he has two expert killers with him at all times.